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Complexity of Maxmin-\(\omega \) Cellular Automata

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Unifying Themes in Complex Systems IX (ICCS 2018)

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

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Abstract

We present an analysis of an additive cellular automaton (CA) under asynchronous dynamics. The asynchronous scheme employed is maxmin-\(\omega \), a deterministic system, introduced in previous work with a binary alphabet. Extending this work, we study the impact of a varying alphabet size, i.e., more than the binary states often employed. Far from being a simple positive correlation between complexity and alphabet size, we show that there is an optimal region of \(\omega \) and alphabet size where complexity of CA is maximal. Thus, despite employing a fixed additive CA rule, the complexity of this CA can be controlled by \(\omega \) and alphabet size. The flavour of maxmin-\(\omega \) is, therefore, best captured by a CA with a large number of states.

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

    Ebrahim L. Patel

Authors
  1. Ebrahim L. Patel
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Correspondence to Ebrahim L. Patel .

Editor information

Editors and Affiliations

  1. New England Complex Systems Institute, Cambridge, MA, USA

    Alfredo J. Morales

  2. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico, Distrito Federal, Mexico

    Carlos Gershenson

  3. New England Complex Systems Institute and University of Massachusetts, Cambridge, MA, USA

    Dan Braha

  4. Department of Electrical Engineering and Computer Science, University of Cincinnati, Cincinnati, OH, USA

    Ali A. Minai

  5. New England Complex Systems Institute, Cambridge, MA, USA

    Yaneer Bar-Yam

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Patel, E.L. (2018). Complexity of Maxmin-\(\omega \) Cellular Automata. In: Morales, A., Gershenson, C., Braha, D., Minai, A., Bar-Yam, Y. (eds) Unifying Themes in Complex Systems IX. ICCS 2018. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-96661-8_10

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